The "Purple box" is a shorthand description for the part of this strategic planning process that occurs following task-force generated recommendations. The shorthand description came from a meeting early in the strategic planning process when User:Sue Gardner was flow charting the process and drew a purple box to represent this time period.
Various other names have been tossed about, for instance: Strategy Taskforce; Discernment Committee; Meta-taskforce. None of these are right, however, because the process will involve the community on a large scale.
Until we can find a better way to describe this part of the process (which will focus on discernment and distilling), we're just calling it the purple box.